Question

I really need help!

In the figure below, ∠DEC ≅ DCE, ∠B ≅ ∠F, and segment DF is congruent to segment DB. Point C is the point of intersection between segment AG and segment BD while point E is the point of intersection between segment AG and segment DF.

http://assets.openstudy.com/updates/attachments/52e82c91e4b0c5eaaf28029d-js555-1390947516398-openstudy1.jpg

Prove ΔABC ≅ ΔGFE.

Answer 1

:( i posted this once a while ago and it never got answered, i hope i get help now.

Answer 2

i wanna help
one sec :o

Answer 3

ok i sketck all congruent in the same color ok ?

Answer 4

ok

Answer 5

nw conceder triangle DEC , it has two congruent angle ,
thats make it isosceles triangle
so
DC=DE right ?

Answer 6

yes.

Answer 7

so since
DF=DE+EF
DB=DC+CB
DF=DB
DE+EF=DC+CB
but DE=DC
then
EF=CB right ?

Answer 8

getting it ?

Answer 9

oh yeah.. now i see

Answer 10

ok good :)
nw
<DCE=<ACB ( vertical angles)
<DEC=<GEF (vertical angles)
but
<DCE=<DEC ( given)
then
<ACB=<GEF

Answer 11

getting it untill nw ?

Answer 12

yea.... 1 second. I had to go do something. I am back now.

Answer 13

ok I get that

Answer 14

ok @Js555 finall step cuz i wanna slp ×_×
u have
<B=<F ( given)
CB=EF (proved)
<ACB=<GEF ( proved )
so u have 2 angle and a side btw (Angle,Side ,Angle)
which is calld ASA
So by ASA( (Angle,Side ,Angle))

ΔABC ≅ ΔGFE ~~DONE^^

Answer 15

THANK YOU SO MUCH!

Answer 16

Ur such a great help. thx!

Answer 17

ur wlc any time ^^